Hang Si

Research Group: Numerical Mathematics and Scientific Computing
Weierstrass Institute for Applied Analysis and Stochastics (WIAS)

Mohrenstr. 39
10117 Berlin,
Germany

Tel: +49(0) 30 20372 446
Fax: +49(0) 30 2044975

si(at)wias-berlin.de

I'm a scientific staff member of the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) in the research group of Numerical Mathematics and Scientific Computing. My work is supported under the research project pdelib of WIAS.


Research Interests

I work in the field of automatic mesh generation, which is a topic about how to partition a geometric domain into a set of simple (non-overlapping) cells. It has wide variaty of applications: mathematical modeling, computer-aided design, visualizations, and so on. It combines different topics from mathematics, computer science, and engineering. It principally requires the studies of discretizing a continuous space in both of its topology and geometry. My primary investigations are the existence and the complexity of such a discretization. Many questions of this study stem from problems in discrete and combinatorial geometry.

The goal of my work is to develope efficient algorithms to automatically generate meshes from arbitrary geometry. It is motivated by solving partial differential equations using numerical methods such as finite element and finite volume methods. I focus on three-dimensional tetrahedral mesh generation. We're developing algorithms to efficiently generate tetrahedral meshes satisfying the Delaunay criterion, which have many nice properties which are important for efficient numerical schemes. We're developing techniques to construct constrained Delaunay tetrahedralizations, quality conforming Delaunay tetrahedralizations for three-dimensional geometries with arbitrarily complicated shapes.

I'm also writing a computer program, TetGen, which is used to implement state-of-the-art methods and algorithms for constructing Delaunay tetrahedralizations and quality tetrahedral meshes. It is one of the best ways to connect "methods" and "results". On the other hand, to provide a robust and efficient meshing tool for solving practical problems in engineering is also very meaningful.


Publications

Here is a list of my recent publications.

Here is my Ph.D thesis: Three dimensional boundary confomring Delaunay mesh generation, Institute of Mathematics, Technische Univerisität Berlin, 2008.

Corrections: The Lemma 3.3.2 and and the Theorem 3.3.4 in my Ph.D thesis are wrong. The correct versions are found in the paper "An analysis of Shewchuk's Delaunay refinement algorithm, In Proc. 18th International Meshing Roundtable, 2009."


Softwares

TetGen is a computer program to generate exact Delaunay tetrahedralizations, exact constrained Delaunay tetrahedralizations, and quality tetrahedral meshes. The latter are quality conforming Delaunay and nicely graded. The source code as well as documentation are freely available.

TetView is a small graphic program used to visualize tetrahedral meshes and piecewise linear complexes. It directly shows the input and output objects (in files) of TetGen on screen. It also has many features for understanding and analysing the viewing objects. It dumps screen contents in high quality encapsulated postscript format. The executable file (on Unix/Linux platforms) is freely available.


A short biography

I was born and grew up in Hangzhou, a city famous for its natural beauty and historical culture in the Zhejiang province of China. I received my B.E. degree in Electrical Engineering of the Hangzhou University (now merged in Zhejiang University) in July, 1994, and my M.S. degree in Computer Science of the Zhejiang University in March, 2002. In between of my two college studies, I've worked as an electrical engineer and a software developer for five years. I jointed WIAS Berlin in October, 2002 and have been working here since then. In August 2008, I got my Ph.D from the Institute für Mathematik in Technische Univerisität Berlin under the supervisor of Prof. Günter Ziegler and Herbert Edelsbrunner.


Hang Si